Mathematics and CAD: Volume 1: Numerical Methods for CAD

by Y. Gardan

Overview

The use of computer-aided design (CAD) systems always involves the introduction of mathematical concepts. It is important, therefore, for any systems designer to have a good grasp of the mathematical bases used in CAD. The choice of mathematical models in a system also has an effect on the overall quality, although this effect may not always be visible to the final user. Depending on whether Bezier or B-spline functions are used for curves and surfaces, for example, the final user even if not a computer scientist will notice a difference. If, for example, one of the control points is modified by the user, in a Bezier-type representation, the curve or surface will tend to be modified overall, but in a B-spline representation, the curve or surface will tend to be modified close to the point, and there only. More possibly harmful, however, is the effect of the mathematical model which has a number of properties invisible and unknown to the final user. In every case a model must be chosen with, it is hoped, the most appropriate characteristics and limits for the task in hand.

Product Details

ISBN-13:	9781468415131
Publisher:	Springer US
Publication date:	02/16/2012
Edition description:	Softcover reprint of the original 1st ed. 1985
Pages:	166
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

1 Basic problems using graphics.- Two-dimensional calculations.- Calculation of perimeters and areas.- Two-dimensional geometric transformations.- Three-dimensional geometric transformations.- Parallel projections and perspectives.- Object modelling.- Conclusions.- References.- 2 Curves and surfaces.- Curves.- Surfaces.- References.- 3 Numerical methods for solving linear and non-linear equations.- Linear equation systems.- Non-linear equation systems.- Non-linear equations.- Conclusions.- References.- Software manuals.- 4 The finite element method.- Examples of variational formulation for boundary value problems.- Internal approximation: Ritz-Galerkin method.- Matching finite elements.- Examples of finite elements.- A two-dimensional example.- Conclusions.- Appendix: the principle behind the finite difference method.- References.